Question

Ross has decided that he wants to build enough retirement wealth that, if invested at 6% per year, will provide him with $3,700 of monthly income for 25 years. To date, he has nothing saved, but he still had 15 years until he retires.

How much money does he need to contribute per month to reach his goal? First compute how much money he will need at retirement, then the monthly contribute to reach that goal. Round final answer 2 decimal places.

Answer 1

Given that,

Ross will require to withdraw PMT = $3700 per month for t = 25 years.

interest rate r = 6% p.a. compounded monthly

So, amount he needed at retirement is calculated using PV formula of annuity:

PV = PMT*(1 - (1+r/n)^-(n*t))/(r/n) = 3700*(1 - (1+0.06/12)^(-12*25))/(0.06/12) = $574265.40

So, amount needed at retirement = $574265.40

To have FV = $574265.40 at retirement, monthly contribution can be calculated using FV formula of annuity:

PMT = FV*(r/n)/((1+r/n)^(n*t) - 1) = 574265.40*(0.06/12)/((1+0.06/12)^(12*15) - 1) = $1974.65

So Ross need to contribute $1974.65 per month to reach the goal.